Understanding Main Effects and Interactions in Factorial Designs
By Dr. Zubair Khalid, DVM, MS, PhD ·
Quick Answer
- Main effects describe the average influence of one factor across all levels of other factors, while interactions show when a factor's effect depends on the level of another factor.
- Plot your data with interaction plots before running statistical tests to visually separate main effects from interaction patterns.
- Factorial designs require balanced replication and careful randomization to avoid confounding interaction estimates with uncontrolled variation.
At a Glance
| Concept | Definition | Biological Example | Interpretation Risk |
|---|---|---|---|
| Main Effect | Average effect of one independent variable across all levels of another variable | Effect of temperature on bacterial growth averaged across two nutrient conditions | Masking a strong effect in one condition with a weak effect in another |
| Interaction Effect | When the effect of one factor changes depending on the level of another factor | Temperature effect on growth appears only in high-nutrient medium | Misinterpreting as a main effect when only one condition shows a response |
| Additive Model | Factors act independently and their combined effect equals the sum of individual effects | Two drugs each reduce cell viability by 20 percent, combined reduction is 40 percent | Assuming additivity without testing interaction terms |
| Synergistic Interaction | Combined effect exceeds the sum of individual effects | Drug A and drug B together reduce viability by 70 percent when each alone reduces it by 20 percent | Overlooking combined effects when analyzing factors separately |
| Antagonistic Interaction | Combined effect is less than the sum of individual effects | One factor suppresses the effect of another | Concluding a factor is ineffective when it is active only in specific conditions |
The Core Problem in Factorial Experiments
Why Single-Factor Thinking Fails in Biological Systems
Biological systems rarely respond to one variable in isolation. A researcher who varies temperature while holding nutrient concentration constant may conclude that temperature has no effect on growth. The same researcher who varies both factors simultaneously may discover that temperature strongly influences growth only when nutrients are abundant. This discrepancy is the central reason factorial designs exist.
The failure mode is common in life-science laboratories. A student tests a drug at one concentration, observes no effect, and moves on. A postdoctoral researcher tests a gene knockout in one growth condition and reports no phenotype. Both conclusions may be correct for the tested condition and incorrect for the broader biological context. The factorial design addresses this by varying multiple factors at once, allowing the researcher to detect effects that depend on context.
The Statistical Foundation of Factorial Designs
A factorial design crosses every level of each factor with every level of every other factor. A two-factor design with three levels of factor A and two levels of factor B produces six treatment combinations. Each combination is a distinct experimental condition. The design allows estimation of the main effect of each factor and the interaction between them.
The main effect of factor A is the average difference in response between levels of A, averaged across all levels of B. The interaction is the extent to which the effect of A differs across levels of B. In a two-factor design, the interaction is the difference between the effect of A at level B1 and the effect of A at level B2.
The statistical model for a two-factor factorial design includes terms for each main effect and one interaction term. The model is written as Y equals the grand mean plus the effect of factor A plus the effect of factor B plus the interaction of A and B plus error. The interaction term captures the non-additive portion of the response.
Why Interactions Are Biologically Meaningful
Interactions are not statistical artifacts. They represent real biological mechanisms. An enzyme may function optimally at a specific temperature and pH combination. A drug may be effective only when a receptor is expressed. A nutrient may be limiting only when another nutrient is present. These are interactions, and they are the rule in biology, not the exception.
The practical consequence is that a researcher who analyzes each factor separately may miss the most important finding in the data. The interaction term can reveal that a factor has a strong effect in one context and no effect in another. This information is essential for designing follow-up experiments and for interpreting the mechanism of action.
Designing a Factorial Experiment
Selecting Factors and Levels
The first decision is which factors to vary and how many levels to use. Two-level designs are the most common because they require the fewest experimental units and provide clear contrasts. Three-level designs allow detection of nonlinear effects but require more units. The choice depends on the research question and the resources available.
A researcher studying bacterial growth might choose temperature and nutrient concentration as factors. Each factor could have two levels, a low and a high value. The design would have four treatment combinations. This is the simplest factorial design and is often called a two-by-two factorial.
The selection of levels is a scientific decision. The levels must be biologically meaningful and must span the range where the researcher expects a response. If the levels are too close together, the experiment may show no effect even when one exists. If the levels are too far apart, the researcher may miss the optimal response region.
Replication and Randomization
Each treatment combination must be replicated to estimate experimental error. The number of replicates depends on the expected variability and the size of the effect the researcher wants to detect. More replicates provide more statistical power but require more resources.
Randomization is the assignment of experimental units to treatment combinations by chance. Randomization protects against confounding by uncontrolled variables. If all replicates of one treatment are measured on the same day, any day-to-day variation is confounded with the treatment effect. Randomization distributes this variation across all treatments.
The researcher should also consider blocking. A block is a group of experimental units that are more similar to each other than to units in other blocks. For example, a researcher might run the experiment in three batches. Each batch is a block. The factorial design can be arranged so that each block contains all treatment combinations, which allows the researcher to account for batch-to-batch variation.
Sample Size Considerations
The sample size for a factorial design depends on the number of factors, the number of levels, the expected effect size, and the variability of the response. A larger sample size increases the power to detect smaller effects and interactions.
The researcher should determine the sample size before starting the experiment. The calculation requires an estimate of the variability of the response, which can come from pilot data or from the published literature. The researcher must also specify the minimum effect size that is biologically meaningful. A statistically significant effect that is too small to matter is not useful.
The sample size calculation for a factorial design is more complex than for a single-factor design because the researcher must consider the power to detect interactions. Interactions often require more replicates than main effects because the interaction is estimated from the difference of differences, which has more variability than a single difference.
Factorial Design Options and Tradeoffs
The full factorial design includes all possible combinations of all factor levels. This design provides the most complete information but can become impractical when the number of factors is large. A design with five factors at two levels each has 32 treatment combinations. A design with six factors has 64 combinations.
The fractional factorial design includes a subset of the treatment combinations. This design requires fewer experimental units but confounds some effects. The researcher must decide which effects are important and which can be confounded. Fractional designs are useful for screening many factors but are not appropriate when interactions are the primary interest.
The researcher should choose the design based on the research question. If the goal is to identify which of several factors has the largest effect, a fractional design may be sufficient. If the goal is to understand the mechanism of interaction between two factors, a full factorial design is necessary.
Analyzing Factorial Data
The Analysis of Variance Approach
The analysis of variance for a factorial design partitions the total variation in the response into components that are attributed to each main effect, the interaction, and the error. The F-test for each component compares the variation explained by that component to the variation that is not explained.
The analysis begins with the calculation of the sum of squares for each factor and the interaction. The sum of squares for factor A measures the variation in the response that is associated with the different levels of A. The sum of squares for the interaction measures the variation that is associated with the combined effect of A and B beyond their individual effects.
The F-statistic for each effect is the ratio of the mean square for that effect to the mean square for error. A large F-statistic indicates that the effect explains more variation than would be expected by chance. The p-value associated with the F-statistic is the probability of observing an F-statistic this large if the effect is zero.
Interpreting Main Effects
A significant main effect for factor A means that the average response differs across the levels of A, averaged across all levels of B. This is the effect of A that is consistent across the other factor.
The main effect is a summary. It does not describe the effect of A at each level of B. If the interaction is significant, the main effect is not a complete description of the data. The researcher must examine the simple effects, which are the effects of A at each level of B.
The main effect is the average of the simple effects. If the interaction is present, the simple effects differ from each other, and the main effect is a weighted average that may not represent any actual condition.
The interaction plot
The interaction plot is a graphical tool for visualizing the interaction. The plot shows the mean response for each combination of the two factors. The x-axis is the level of factor A, and the lines represent the levels of factor B.
If the lines are parallel, there is no interaction. The effect of A is the same at each level of B. If the lines cross or diverge, there is an interaction. The effect of A differs across the levels of B.
The interaction plot is a diagnostic tool. It should be examined before the statistical test to identify the pattern of the interaction. The plot can also reveal whether the interaction is synergistic or antagonistic.
Practical Workflow for a Factorial Experiment
Step 1: Define the Research Question
The research question must specify the factors, the levels, and the response. The question should be specific enough to guide the design. A vague question such as "does temperature affect growth" is not sufficient. The question should be "does temperature affect growth at two nutrient concentrations" or "does the effect of temperature depend on nutrient concentration."
Step 2: Select the Design
The design is selected based on the research question and the available resources. A full factorial design is appropriate when the interaction is the primary interest. A fractional design is appropriate for screening. The design must include the factors and levels that are necessary to answer the research question.
Step 3: Determine the Sample Size
The sample size is determined by the expected effect size, the variability of the response, and the desired power. The researcher must specify the minimum effect size that is worth detecting. The power analysis should be conducted before the experiment begins.
Step 4: Randomize and Block
The experimental units are randomly assigned to the treatment combinations. If the experiment is run in batches, the batches are blocks, and the treatment combinations are randomly assigned within each block.
Step 5: Collect the Data
The response is measured for each experimental unit. The data are recorded in a structured format that includes the factor levels and the response. The data must be checked for errors and outliers.
Step 6: Analyze the Data
The data are analyzed using the analysis of variance. The main effects and the interaction are tested. The interaction plot is examined to interpret the pattern of the interaction.
Step 7: Interpret the Results
The results are interpreted in the context of the research question. A significant interaction means that the effect of one factor depends on the other factor. The main effects are interpreted only if the interaction is not significant.
Records and Measurements
What to Record
The record for a factorial experiment must include the factor levels for each experimental unit, the response measurement, and the date and time of the measurement. The record must also include any observations about the experimental conditions, such as temperature fluctuations or equipment problems.
The record should be detailed enough that another researcher can reproduce the experiment. The record should include the exact protocol for preparing the experimental units, the measurement method, and the data analysis.
Data Quality Checks
The data should be checked for errors before the analysis. The check includes verifying that the factor levels are correct, that the response values are within the expected range, and that there are no missing values.
The data should also be checked for outliers. An outlier is a value that is far from the other values in the same treatment combination. The outlier may be a measurement error or a real biological variation. The researcher must decide whether to include the outlier in the analysis.
The Role of the Laboratory Notebook
The laboratory notebook is the primary record of the experiment. The notebook should include the research question, the design, the protocol, the data, and the analysis. The notebook should be written in a way that another researcher can follow.
The notebook is also the record of the decisions that were made during the experiment. If the researcher decided to exclude an outlier, the decision and the reason should be recorded. If the researcher changed the protocol, the change should be recorded.
Common Failure Patterns in Factorial Experiments
Interpreting Main Effects When the Interaction Is Significant
The most common error is to interpret the main effect of a factor when the interaction is significant. The main effect is the average effect across the levels of the other factor. If the interaction is significant, the effect of the factor is not consistent across the levels of the other factor. The main effect is a misleading summary.
The correct interpretation is to examine the simple effects. The simple effect of factor A at each level of factor B is the effect of A within that level. The simple effects are the most informative description of the data when the interaction is significant.
Using Too Few Replicates
A factorial design with too few replicates has low power to detect interactions. The researcher may conclude that there is no interaction when the interaction is present. The power analysis should be conducted before the experiment to determine the number of replicates.
Confounding the Treatment with the Time of Measurement
If all replicates of one treatment combination are measured at the same time, the treatment effect is confounded with the time effect. The randomization of the measurement order prevents this confounding.
Ignoring the Blocking Factor
If the experiment is conducted in batches, the batch is a blocking factor. The analysis must include the block as a factor. If the block is ignored, the variation between blocks is included in the error, which reduces the power to detect the treatment effects.
Overlooking the Interaction Plot
The interaction plot is a simple and effective tool for detecting the interaction. The researcher should always create the interaction plot before the statistical test. The plot can reveal the pattern of the interaction and can help the researcher interpret the statistical results.
Limitations of Factorial Designs
The Number of Treatment Combinations
The number of treatment combinations increases rapidly with the number of factors and levels. A design with four factors at three levels each has 81 treatment combinations. The researcher must have the resources to run all of the combinations.
The Interpretation of Higher-Order Interactions
Three-way interactions require examining each two-way relationship separately at every level of the third factor - a conditional-on-conditional decomposition requiring systematic panel-by-panel visualisation. The three-way interaction means that the two-way interaction differs across the levels of the third factor. The interpretation requires the examination of the simple interaction effects.
The Assumption of the Analysis of Variance
The analysis of variance assumes that the residuals are normally distributed and that the variances are equal across the treatment groups. The researcher should check these assumptions before interpreting the results. If the assumptions are violated, the researcher may need to transform the data or use a different analysis.
The Generalizability of the Results
The results of a factorial experiment are generalizable only to the levels of the factors that were tested. If the researcher tested temperature at 20 and 30 degrees Celsius, the results do not apply to 40 degrees Celsius. The researcher must be careful not to overgeneralize the results.
Quality Controls and Welfare Considerations
The Quality Control of the Measurement
The measurement method must be consistent across all experimental units. The instrument must be calibrated before the experiment and checked during the experiment. The measurement should be performed by the same person or by people who have been trained to the same standard.
The Welfare of the Experimental Subjects
If the experimental subjects are animals, the welfare of the animals must be considered. The experiment must be approved by the institutional animal care and use committee. The researcher must follow the guidelines for the care and use of laboratory animals.
The Biosafety of the Experiment
If the experiment involves biological agents, the researcher must follow the biosafety guidelines. The researcher must use the appropriate containment and personal protective equipment. The researcher must also follow the institutional biosafety committee requirements.
The Reporting of the Results
The results of the experiment should be reported in a way that is transparent and complete. The report should include the design, the sample size, the analysis, and the limitations. The report should follow the reporting guidelines for the specific type of study. The EQUATOR Network provides a list of reporting guidelines for different study types.
Documentation and Reproducibility
The Data Management Plan
The data management plan describes how the data will be collected, stored, and shared. The plan should be written before the experiment begins. The plan should include the file format, the storage location, and the backup procedure.
The NIH Data Management and Sharing Policy articulates federal requirements for comprehensive data preservation, metadata formatting, and open repository deposition across all biomedical studies.
The Researcher Identity
The researcher should maintain a record of their research output. The ORCID for Researchers provides a unique identifier for the researcher. The identifier can be used to link the researcher to their publications and datasets.
The Publication Ethics
The publication of the results should follow the ethical standards for publication. The Committee on Publication Ethics provides the core practices for publication ethics, including authorship, peer review, and data.
The Funding and Grant Context
The researcher should be aware of the funding requirements for the research. The NIH Grants and Funding provides the official information about the NIH grant policy, application, and review.
Professional Escalation Criteria
When to Consult a Statistician
The researcher should consult a statistician when the design is complex, when the analysis is not straightforward, or when the assumptions of the analysis are violated. The statistician can help with the design, the sample size, and the analysis.
When to Consult a Biosafety Officer
The researcher should consult a biosafety officer when the experiment involves biological agents that require a higher level of containment. The biosafety officer can help with the risk assessment and the containment.
When to Consult the Institutional Review Board
The researcher should consult the institutional review board when the experiment involves human subjects. The review board must approve the study before the research begins.
When to Consult the Institutional Animal Care and Use Committee
The researcher should consult the institutional animal care and use committee when the experiment involves animals. The committee must approve the study before the research begins.
A Practical Decision Framework for Interpreting Significant Interactions
The Problem of Deciding What to Report
A researcher who finds a significant interaction faces a decision that the statistical output does not answer. The F-test confirms that the effect of one factor depends on the level of another factor, but it does not say which simple effects matter, how large the differences are, or how to present the findings to a reader. Many researchers respond by reporting the main effects and the interaction in the same paragraph, which leaves the reader uncertain about the actual biological pattern. This section provides a structured decision framework that moves from the statistical result to a defensible interpretation.
The framework has four stages. First, verify the interaction is real and not an artifact of the data. Second, estimate the simple effects and their precision. Third, classify the interaction pattern as synergistic, antagonistic, or qualitative. Fourth, decide which effects to report as the primary findings. Each stage has specific records, calculations, and escalation criteria.
Stage 1: Verify the Interaction Before Interpretation
The first decision is whether the interaction is a genuine biological pattern or a consequence of data problems. A significant interaction can arise from a few causes that are not biological. Unequal variances across treatment groups can produce a spurious interaction. An outlier in one treatment combination can pull the interaction term toward significance. A coding error in the factor levels can create a pattern that looks like an interaction.
The verification step has three checks. The first check is the residual plot. Plot the residuals from the analysis of variance against the fitted values. If the spread of residuals increases with the fitted values, the variance is not constant. The interaction test assumes equal variances across all treatment combinations. A variance-stabilizing transformation, such as the logarithm for count data or the square root for count data with small values, may be needed before the interaction test is meaningful.
The second check is the outlier examination. For each treatment combination, calculate the mean and the standard deviation of the replicates. Identify any value that is more than three standard deviations from the mean of its own treatment combination. Examine the laboratory notebook for that value. If the value is a measurement error, such as a misread instrument or a mislabeled tube, correct the record and rerun the analysis. If the value is a genuine biological observation, keep it in the analysis and note it in the report.
The third check is the interaction plot with individual data points. The interaction plot of means can hide the variability within each treatment combination. Plot the individual replicate values on the same axes as the interaction plot. This plot shows whether the interaction pattern is consistent across replicates or driven by a single extreme value. If the pattern disappears when the extreme value is removed, the interaction is not robust and should be interpreted with caution.
Stage 2: Estimate Simple Effects and Their Precision
When the interaction is verified, the next step is to estimate the simple effects. A simple effect is the effect of one factor at a single level of the other factor. In a two-by-two design, there are two simple effects of factor A, one at each level of factor B. The simple effect is the difference between the two levels of A within that level of B.
The simple effects are the building blocks of the interaction interpretation. The interaction is the difference between the two simple effects. If the simple effect of A at B1 is 10 units and the simple effect of A at B2 is 4 units, the interaction is 6 units. The interaction test asks whether this difference of 6 units is larger than what would be expected by chance.
The precision of each simple effect is important. A simple effect that is large but imprecise is not a reliable finding. The standard error of a simple effect is calculated from the mean square error of the analysis of variance. The confidence interval for each simple effect shows the range of plausible values. A simple effect with a confidence interval that includes zero is not distinguishable from no effect.
The researcher should compute the confidence intervals for all simple effects and present them in a table or a figure. The confidence intervals allow the reader to see which simple effects are reliable and which are not. This is more informative than a single p-value for the interaction.
Stage 3: Classify the Interaction Pattern
The classification of the interaction pattern guides the interpretation. There are three common patterns in biological experiments.
The first pattern is the quantitative interaction. The simple effects have the same direction but different magnitudes. For example, factor A increases the response at both levels of factor B, but the increase is larger at the high level of B. The interaction is significant because the magnitudes differ. The biological interpretation is that factor B modulates the strength of factor A but does not change its direction.
The second pattern is the qualitative interaction. The simple effects have opposite directions. For example, factor A increases the response at the low level of factor B and decreases the response at the high level of factor B. The interaction is significant because the directions differ. The biological interpretation is that factor B changes the nature of the factor A effect. This pattern is the most important to identify, because the main effect of factor A is zero or misleading when the simple effects cancel.
The third pattern is the effect-only interaction. One simple effect is large and the other is near zero. For example, factor A has a strong effect at the high level of factor B and no effect at the low level of factor B. The interaction is significant because the effect appears only in one condition. The biological interpretation is that factor B is a permissive condition for factor A.
The classification is a scientific judgment, not a statistical test. The researcher should classify the pattern based on the estimated simple effects and their confidence intervals. The classification should be recorded in the laboratory notebook and stated in the report.
Stage 4: Decide What to Report as the Primary Findings
The final stage is the decision about what to report. The decision depends on the classification from Stage 3.
For a quantitative interaction, the researcher should report both simple effects and the interaction. The main effect of each factor is still useful because it describes the average direction of the effect. The interaction describes the difference in magnitude. The report should state that factor A has a positive effect at both levels of factor B and that the effect is stronger at the high level of factor B.
For a qualitative interaction, the researcher should not report the main effects as the primary findings. The main effect of factor A is the average of the positive and negative simple effects, which may be close to zero. Reporting the main effect would mislead the reader. The report should state the simple effects separately and emphasize that the direction of the effect depends on the level of factor B.
For an effect-only interaction, the researcher should report the simple effect that is present and the simple effect that is absent. The report should state that factor A has an effect only when factor B is at the high level. The main effect of factor A is a weighted average of the two simple effects and is not a complete description.
The report should include the interaction plot with the simple effects and their confidence intervals. The plot is the most direct way to communicate the pattern to the reader. The report should also include the classification of the interaction pattern and the biological interpretation.
A Record System for Interaction Decisions
The decision framework requires a record system that captures the reasoning at each stage. The record should be part of the laboratory notebook and should include the following items.
The first item is the verification record. This includes the residual plot, the outlier examination, and the corrected data. The record should state whether the interaction was verified or whether the data required correction.
The second item is the simple effect table. The table should include the simple effect estimate, the standard error, and the confidence interval for each simple effect. The table should also include the interaction estimate and its confidence interval.
The third item is the classification statement. The record should state whether the interaction is quantitative, qualitative, or effect-only. The statement should include the biological reasoning for the classification.
The fourth item is the reporting decision. The record should state which effects are reported as the primary findings and which are reported as secondary. The record should also state the exact wording that will be used in the report.
The record should be written before the final analysis is run. This prevents the researcher from changing the decision after seeing the results. The record is a commitment to a pre-specified interpretation plan.
Common Failure Patterns in the Decision Framework
The decision framework has its own failure patterns. The first failure is skipping the verification stage. A researcher who sees a significant interaction and immediately interprets it may be interpreting an artifact. The verification stage takes a small amount of time and prevents a large amount of misinterpretation.
The second failure is using the main effect to describe a qualitative interaction. The main effect is the average of the simple effects. In a qualitative interaction, the average is not a meaningful summary. The researcher must report the simple effects.
The third failure is ignoring the confidence intervals of the simple effects. A simple effect that is large but has a wide confidence interval is not a reliable finding. The researcher must report the precision of the simple effects.
The fourth failure is not recording the classification decision. The classification is a scientific judgment that should be documented. The record allows another researcher to understand the reasoning and to challenge the classification if needed.
When to Escalate to a Statistician
The decision framework is designed for a researcher with a basic understanding of analysis of variance. Some situations require escalation to a statistician. The researcher should consult a statistician when the interaction is qualitative and the simple effects have opposite directions. This pattern is rare and may indicate a problem with the measurement scale. The statistician can help determine whether the interaction is real or an artifact of the scale.
The researcher should also consult a statistician when the interaction is a three-way interaction. Three-way interactions require examining each two-way relationship separately at every level of the third factor - a conditional-on-conditional decomposition requiring systematic panel-by-panel visualisation. The statistician can help with the simple interaction effects and the presentation.
The researcher should consult a statistician when the variance is not constant across the treatment combinations and the transformation does not fix the problem. The statistician can recommend an alternative analysis, such as a generalized linear model or a mixed model.
The escalation criteria are part of the decision framework. The researcher should not attempt to interpret a complex interaction without the appropriate statistical support. The Research Methods Resources from the National Library of Medicine provides access to authoritative books on research methods and statistical analysis that can support the interpretation.
The Role of the Decision Framework in the Research Report
The decision framework is not a statistical test. It is a structured approach to interpretation. The framework ensures that the researcher has verified the interaction, estimated the simple effects, classified the pattern, and chosen the reporting strategy. The framework also ensures that the decisions are recorded and can be reviewed.
The research report should include the decision framework as part of the methods and results. The methods section should state that the interaction was verified, the simple effects were estimated, and the pattern was classified. The results section should present the simple effects and the interaction plot. The discussion section should interpret the pattern in the biological context.
Manuscript reporting should conform to the validated checklist appropriate for the study design - CONSORT for RCTs, STROBE for observational studies, PRISMA for systematic reviews, or ARRIVE for animal experiments.
The decision framework is a practical tool for the researcher who wants to avoid the common error of misinterpreting main effects when the interaction is significant. The framework provides a clear path from the statistical output to a defensible biological interpretation.
Frequently Asked Questions
How is an isolated factor main effect statistically distinguished from a cross-factor interaction term?
A main effect quantifies the average influence of a single factor on the response variable, computed by averaging across all levels of every other factor in the experiment.
How do I know if my data have an interaction?
You can create an interaction plot. The plot shows the mean response for each combination of the two factors. If the lines are parallel, there is no interaction. If the lines cross or diverge, there is an interaction. The statistical test for the interaction is the F-test in the analysis of variance.
Why is it important to use a factorial design instead of testing one factor at a time?
Testing one factor at a time cannot detect interactions. If the effect of one factor depends on the level of another factor, the single-factor experiment will miss the effect. The factorial design varies all factors simultaneously, which allows the detection of the interaction.
What is a two-by-two factorial design?
A two-by-two factorial design has two factors, each with two levels. The design has four treatment combinations. This is the simplest factorial design and is used to test the main effects of two factors and their interaction.
How many replicates do I need for a factorial design?
The number of replicates depends on the expected variability, the effect size, and the desired power. The power analysis should be conducted before the experiment. The power analysis requires the specification of the minimum effect size that is worth detecting.
What should I do if my interaction is significant?
If the interaction is significant, you should not interpret the main effects. You should examine the simple effects, which are the effects of one factor at each level of the other factor. The simple effects describe the effect of the factor in each condition.
What is the difference between a full factorial and a fractional factorial design?
A full factorial design includes all combinations of all factor levels. A fractional factorial design includes a subset of the combinations. The fractional design requires fewer experimental runs but confounds some effects. The fractional design is used for screening studies.
How do I report the results of a factorial experiment?
The report should include the design, the sample size, the analysis, and the results. The report should follow the reporting guidelines for the type of study. The EQUATOR Network provides a list of reporting guidelines.
Using the Evidence
| Source | Best use in this topic | Important limitation |
|---|---|---|
| Research Methods Resources | official guidance | Check the linked page for current local requirements |
| EQUATOR Network | official guidance | Check the linked page for current local requirements |
| Core Practices | official guidance | Check the linked page for current local requirements |
Related Diagnostic Guides
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References and Further Reading
- Research Methods Resources. National Library of Medicine.
- EQUATOR Network. EQUATOR Network.
- Core Practices. Committee on Publication Ethics.
- NIH Grants and Funding. National Institutes of Health.
- ORCID for Researchers. ORCID.
- Data Management and Sharing Policy. National Institutes of Health.
- Laboratory Biosafety Manual. World Health Organization.
- NCBI Literature Resources. National Center for Biotechnology Information.
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This article is educational and does not replace validated laboratory procedures, institutional biosafety review, manufacturer instructions, or professional interpretation.